Optimizing extension techniques for discovering non-algebraic matroids

Identifier:  imarina:9468630

Handle: https://hdl.handle.net/20.500.11797/imarina9468630

Authors:  Bamiloshin, M; Farràs, O

Abstract:
In this work, we revisit some combinatorial and information-theoretic extension techniques for detecting non-algebraic matroids. These are the Dress-Lov & aacute;sz and Ahlswede-K & ouml;rner extension properties. We provide optimizations of these techniques to reduce their computational complexity, finding new non-algebraic matroids on 9 and 10 points. In addition, we use the Ahlswede-K & ouml;rner extension property to find better lower bounds on the information ratio of secret-sharing schemes for ports of non-algebraic matroids.